# Article

Full entry | PDF   (0.2 MB)
Keywords:
multifunction; convex subdifferential; extremal periodic solution; Moreanu-Yosida approximation.
Summary:
We consider first order periodic differential inclusions in $\mathbb {R}^N$. The presence of a subdifferential term incorporates in our framework differential variational inequalities in $\mathbb {R}^N$. We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.
References:
[1] Bader R.: A topological fixed point theory for evolutions inclusions. Z. Anal. Anwendungen 20 (2001), 3–15. MR 1826317
[2] Bourgain J.: An averaging result for $l^1$-sequences and applications to weakly conditionally compact sets in $L^1(X)$. Israel J. Math. 32 (1979), 289–298. MR 0571083
[3] Cornet B.: Existence of slow solutions for a class differential inclusions. J. Math. Anal. Appl. 96 (1983), 130–147. MR 0717499
[4] De Blasi F. S., Gorniewicz L., Pianigiani G.: Topological degree and periodic solutions of differential inclusions. Nonlinear Anal. 37 (1999), 217–245. MR 1689752 | Zbl 0936.34009
[5] De Blasi F. S., Pianigiani G.: Nonconvex valued differential inclusions in Banach spaces. J. Math. Anal. Appl. 157 (1991), 469–494. MR 1112329
[6] Haddad G., Lasry J.-M.: Periodic solutions of functional differential inclusions and fixed points of $\gamma$-selectionable correspondences. J. Math. Anal. Appl. 96 (1983), 295–312. MR 0719317
[7] Halidias N., Papageorgiou N. S.: Existence and relaxation results for nonlinear second order multivalued boundary value problems in $\mathbb{R^N}$. J. Differential Equations 147 (1998), 123–154. MR 1632661
[8] Henry C.: Differential equations with discontinuous right hand side for planning procedures. J. Econom. Theory 4 (1972), 545–551. MR 0449534
[9] Hu S., Kandilakis D., Papageorgiou N. S.: Periodic solutions for nonconvex differential inclusions. Proc. Amer. Math. Soc. 127 (1999), 89–94. MR 1451808 | Zbl 0905.34036
[10] Hu S., Papageorgiou N. S.: On the existence of periodic solutions for nonconvex valued differential inclusions in $\mathbb{R^N}$. Proc. Amer. Math. Soc. 123 (1995), 3043–3050. MR 1301503
[11] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis. Volume I: Theory. Kluwer, Dordrecht, The Netherlands (1997). MR 1485775 | Zbl 0887.47001
[12] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis. Volume II: Applications. Kluwer, Dordrecht, The Netherlands (2000). MR 1741926 | Zbl 0943.47037
[13] Li C., Xue X.: On the existence of periodic solutions for differential inclusions. J. Math. Anal. Appl. 276 (2002), 168–183. MR 1944344 | Zbl 1020.34015
[14] Macki J., Nistri P., Zecca P.: The existence of periodic solutions to nonautonomous differential inclusions. Proc. Amer. Math. Soc. 104 (1988), 840–844. MR 0931741 | Zbl 0692.34042
[15] Plaskacz S.: Periodic solutions of differential inclusions on compact subsets of $\mathbb{R^N}$. J. Math. Anal. Appl. 148 (1990), 202–212. MR 1052055

Partner of